My understanding is that I should look only at the Pr < Tau column, ignoring the Pr < Rho column.

I should look at the types in the order:

Trend

Single Mean

Zero Mean

If I can reject the null hypothesis at Pr < Tau in the Trend row, then I don't need to bother looking at Single Mean or Zero Mean. In the provided example, this is the case with .0174 being less than .05.

Rejecting the Trend hypothesis indicates that there is a high probability that there is no unit root and that the process is trend stationary.

Rejecting the Single Mean hypothesis indicates that there is a high probability that there is no unit root and that the process is stationary, but the mean is offset by some constant from 0.

Rejecting the Zero Mean hypothesis indicates that there is a high probability that there is no unit root and that the process is stationary with the mean being 0.

Did I say anything that is false or shows a superficial understanding? Is there anything I'm missing?